Formulas 2

[OTBRandy]

G-Day,

Was looking for the formula to calculate "Velocity vs Pounds per square inch of pressure"

 

[CESSNA1]

G-DAY:

The other question here is "in what"? Typically the generalized equation is P=RQ Where P is the pressure drop through an object, such as a pipe. R is the resistance, and Q is the flow rate. The real problem here is "R" which can be non-linear and dependent on many parameters such as smootheness, shape, obstructons, Reynolds number, etc.

Regards
Dave

 

[OTBRandy]

Okay... need to be more specific...
Looking for PSI, impact Pressure, say on an aircraft windshield or wing leading edge, vs velocity...
Example: Aircraft at 0 Mph, pressure 0 (relative to standing atmospheric pressure). Aircraft moving at say 60 Mph, what is the impact pressure on a 180 degree flat surface at that velocity...
Working on a RAT upgrade for my Cessna 172 to assist in my power use for my on board equipment... This RAT is internal with a Ram Air scoop in the slipstream under the aircraft... Need to compute the necessary size, compared to pressure of compression at velocity, to determine size of internal turbine system...

Randy

 

[CESSNA1]

OTBRANDY: Sorry I got your name wrong, I apologize. This is not a total matter of pressure. What you are looking at is energy. How much energy is in the moving airstream, how much energy you need, and how much energy the RAT can extract from the air stream.

The airstream energy is 0.5 * M * V^2

E = #-ft/sec
M = mass flow (#/sec X 1/32.159)
V = velocity (ft/sec)

Consider the RAT as a stream tube where there is "E" energy in the airstream going in, Some energy is extracted by the RAT and other losses and the residual energy is exhausted out the back.

There should be information with the RAT to help here.

Regards
Dave

 

[sailoday28]

for perfect gas isentropic flow
ratio of impact to free stream pressure=
[1 + (gamma-1)/2*M^2]^[{gamma-1}/gamma]
M=Mach no.
gamma= ratio of specific heats ideally air gamma=1.4

 

[sreid]

A really old fluid mechanics book gives a drag coefficient (Cd) of about one for Reynold's numbers between 2000 and 1,000,000. The Reynold's number reference dimension is the length of a side of the square.

Clearly the pressure isn't constant on the plate face but you can get the average pressure (Force/Area).

 

[sreid]

Stagnation (dynamic or impact pressure) is given by

Ps = Po + Rho x V^2/2

 

[btrueblood]

sreid, you got your equation subscripts mixed.

Ps = static pressure
Po = total pressure or impact pressure

Po = Ps + (1/2)*[ρ]*V[sup]2[/sup]

Where [ρ] is mass density (kg/m[sup]3[/sup])
V is velocity (m/s).

Sailoday's equation gives the same answers (within 5%) as this equation for Mach numbers below 0.3, which is where the 172 usually flies.

 

[sailoday28]

btrueblood and sreid-----your equation is for incompressible flow which as you have observed for the compressible one are compatible at low Mach nos.